The present invention relates generally to the field of printing and specifically to color separation, calibration and control of printer actuation parameters. It discloses a new comprehensive model for predicting the color of patches printed with standard and/or non-standard inks. It represents an improvement over an initial model (see U.S. patent application Ser. No. 10/440,355, “Reproduction of Security Documents and Color Images with Metallic Inks, filed 19th of Jun. 2003, inventors R. D. Hersch, P. Emmel, F. Collaud, and the paper “Reproducing Color Images With Embedded Metallic Patterns” by R. D. Hersch, F. Collaud, P. Emmel, Siggraph 2003 Annual Conference Proceedings, ACM Trans. of Graphics, Vol 22, No. 3, to be published 27th of Jul. 2003), which is used in the context of printing with metallic inks.
Being able to calibrate and control printers and printing presses is a challenge, since until now no comprehensive model exists which is capable of predicting accurately the spectra of polychrome color patches printed on paper. Existing methods for color printer characterization and calibration rely either on experimental approaches which require the measurement of hundreds of patches in order to create a correspondence between input colorimetric values (e.g. CIE-XYZ or CIE-LAB) and ink coverage values, or they rely on model-based, partly empirical methods. In respect to experimental approaches, the correspondence between input colorimetric values (e.g. CIE-XYZ or CIE-LAB) and ink surface coverages can be established by regression methods (see H. R. Kang, Color Technology for Electronic Imaging Devices, SPIE Optical Engineering Press, 1997, pp. 55-63) or by interpolation in 3D space (see S. I. Nin, J. M. Kasson, W. Plouffe, Printing CIELAB images on a CMYK printer using tri-linear interpolation, Conf. Color Copy and Graphic Arts, 1992, SPIE Vol. 1670, 316-324).
Model-based methods include the spectral Neugebauer model which predicts the reflection spectrum R(λ) of a color halftone patch as the weighted sum of the reflection spectra Ri of its individual colorants, where the weighting factors are their fractional area coverages ai (H. R. Kang, “Color Technology for Electronic Imaging Devices”, SPIE Optical Engineering Press, 1997, pp. 8-12, hereinafter referenced as the “Neugebauer model”).
                              R          ⁡                      (            λ            )                          =                              ∑            i                    ⁢                                    a              i                        ·                                          R                i                            ⁡                              (                λ                )                                                                        (        1        )            
In the case of independently printed cyan, magenta and yellow inks of respective coverages c, m, y, the fractional area coverages of the individual colorants are closely approximated by the Demichel equations which give the probability of a point to be located within a given colorant area (see M. E. Demichel, Procidt, Vol. 26, 1924, 17-21, 26-27 and D. R. Wyble, R. S. Berns, “A Critical Review of Spectral Models Applied to Binary Color Printing”, Journal of Color Research and Application, Vol. 25, No. 1, February 2000, 4-19):white: aw=(1−c)·(1−m)·(1−y)cyan: ac=c·(1−m)·(1−y)magenta: am=(1−c)·m·(1−y)yellow: ay=(1−c)·(1−m)·yred: ar=(1−c)·m·ygreen: ag=c·(1−m)·yblue: ab=c·m·(1−y)black: ak=c·m·y  (2)where aw, ac, am, ay, ar, ag, ab, ak are the respective fractional areas of the colorants white, cyan, magenta, yellow, red (superposition of magenta and yellow), green (superposition of yellow and cyan), blue (superposition of magenta and cyan) and black (superposition of cyan, magenta and yellow).
Since the Neugebauer model does not take explicitly into account the propagation of light due to internal reflections (Fresnel reflections) at the paper-air interface, its predictions are not accurate (see H. R. Kang, Applications of color mixing models to electronic printing, Journal of Electronic Imaging, Vol. 3, No. 3, July 1994, 276-287). Yule and Nielsen (see H. R. Kang, “Color Technology for Electronic Imaging Devices”, SPIE Optical Engineering Press, 1997, pp. 43-45, original reference: J. A. C. Yule, W. J. Nielsen, The penetration of light into paper and its effect on halftone reproductions, Roc. TAGA, Vol. 3, 1951, 65-76) expanded the Neugebauer model by modelling the non-linear relationship between colorant reflection spectra and predicted reflectance by an empirical power function, whose exponent n is fitted according to a limited set of measured patch reflectances.
                                          R            tot                    ⁡                      (            λ            )                          =                              (                                          ∑                i                            ⁢                                                a                  i                                ·                                                                            R                      i                                        ⁡                                          (                      λ                      )                                                                            1                    n                                                                        )                    n                                    (        3        )            
While offering a better accuracy than other existing models (see H. R. Kang, Applications of color mixing models to electronic printing, Journal of Electronic Imaging, Vol. 3, No. 3, July 1994, 276-287), the Yule-Nielsen model does not incorporate explicit variables for the ink transmission spectra and therefore it cannot be used to predict relative ink thickness values.
In the prior art, the control of printer actuation parameters affecting the printed output such as the effective dot size or the ink thickness, are carried out by means which are completely independent of the printer calibration. Ink thickness in printing presses is generally controlled by relying on density measurements of solid ink or halftone patches. For example, U.S. Pat. No. 4,852,485 (Method of operating an autotypical color offset machine, Inventor F. Brunner, issued Aug. 1, 1989) teaches a method to regulate the feeding of inks in a printing machine by relying on density measurements. As another example, U.S. Pat. No. 5,031,534 (Method and apparatus for setting up for a given print specification defined by a binary value representing solid color density and dot gain in an autotype printing run, inventor F. Brunner, issued Jul. 16, 1991) teaches a method for establishing a print specification relying on a selected solid color density and a dot gain value, the dot gain value also being obtained by densitometric measurements.
In respect to printing with non-standard inks, such as Pantone inks, U.S. Pat. No. 5,734,800 (Six color process system, inventor R. Herbert, issued Mar. 31, 1998) teaches a method for printing with fluorescent inks. However that method implies a large number (many hundreds) of measurements of patches printed with the combinations of the basic inks at different coverages. These measurements allow to build a lookup table converting between CIE-XYZ values and coverages of selected inks. In contrast, the comprehensive spectral prediction model disclosed in the present invention can be used to carry out the color separation and determine the amounts of non-standard inks which need to be printed in order to yield a desired CIE-XYZ calorimetric value. Relying on the comprehensive spectral prediction model allows to reduce considerably the number of measured patches.
The present invention discloses a new spectral prediction model which relies on a weighted average between one part behaving as the Clapper-Yule model (see F. R. Clapper and J. A. C. Yule, The Effect of Multiple Internal Reflections on the Densities of Half-tone Prints on Paper, Journal of the Optical Society of America, Volume 43, Number 7, July 1953, pp. 600-603) and another part behaving as the spectral Neugebauer model, extended to include multiple internal reflections at the paper-air boundary (Saunderson correction: see J. L. Saunderson, Calculation of the color pigmented plastics, Journal of the Optical Society of America, Vol. 32, 1942, 727-736). In addition, the disclosed comprehensive spectral prediction model includes new methods for computing the physical (mechanical) dot surface coverage, hereinafter also called effective surface coverage.
In the disclosed comprehensive spectral prediction model, physical dot surface coverages and ink transmittances are explicit elements of the model. It becomes therefore possible, according to Beer's law, to deduce from two transmittances the corresponding increase or reduction in ink thickness. Ink thickness is an important print parameter for the control of the flow of ink in printers.
In addition, the disclosed comprehensive spectral prediction model is useful for printer calibration, i.e. for establishing a correspondence between input calorimetric values (e.g. CIE-XYZ or CIE-LAB) and ink coverage values. In respect to state of the art printer calibration methods, calibration methods relying on the disclosed spectral prediction model need only a limited set of measured patches (e.g. 44 patches when printing with 3 inks). Recalibration, which is required when another type of paper is used, or when a slightly different set of inks is used, becomes a simple operation.
Finally, since the disclosed spectral prediction model can predict the color of the superposition of standard and non-standard inks, it may be used to carry out the color separation when printing with non-standard inks, such as Pantone inks. It may also be used for controlling the printer when printing with non-standard inks.